arXiv subjects
Publications and source records attributed to Cristodor Ionescu.
We notice the connection between almost Cohen-Macaulay rings and the Cohen-Macaulay defect. We introduce a Serre-type condition for modules, that is connected to the Cohen-Macaulay defect in the same way that the condition $(S_n)$ is connected to Cohen-Macaulay modules.
Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.
We prove that the Andre-Quillen homology and cohomology modules of F-finite Z(p)-algebras are finitely generated.
We investigate the almost Cohen-Macaulay property and the Serre-type condition $(C_n),\ n\in\mathbb{N},$ for noetherian algebras and modules. More precisely, we find permanence properties of these conditions with respect to tensor products and direct limits.
For pairs of integers (n,m) and (d,e) satisfying some nedesary conditions, we construct a local flat ring morphism of noetherian local rings u:A -->B such that dim(A)=n, depth(A)=d, dim(B)=m, depth(B)=e.
Some interesting properties of almost Cohen-Macaulay rings are investigated and a Serre type property connected with this class of rings is studied.
Let B be a ring and $A=B[X,Y]/(aX^2+bXY+cY^2-1)$ where $a,b,c\in B$. We study the smoothness of A over B, and the regularity of B when B is a ring of algebraic integers.
Let $u:A\to B$ be a morphism of noetherian local rings. We obtain smoothness criteria for algebras with differential bases, in the case of rings containing a field of characteristic $p>0.$ We also give smoothness criteria for reduced morphisms.
We compute some algebraic invariants (e.g. depth, Castelnuovo - Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products.
We compute the first Andre-Quillen homology modules for the simple over-rings of integrally closed domains and study an ideal theoretic condition arising from the vanishing of the first homology module.
Recently, the regular local rings of prime characteristic were characterized in terms of the finiteness of injective dimension of the Frobenius map. We obtain relative versions of this result.